Quadratic Problems - Projectile Motion

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How to solve projectile motion word problems using quadratic equations?

Solving projectile problems with quadratic equations
Example: A projectile is launched from a tower into the air with initial velocity of 48 feet per second. Its height, h, in feet, above the ground is modeled by the function
h = -16t² + v₀t + 64
where t is the time, in seconds, since the projectile was launched and v₀ is the initial velocity.
(a) How long is the projectile in the air?
(b) When did it reach its maximum height?
(c) What was its maximum height? Solving a Projectile Problem Using Quadratics
Example: Larry throws a rock in the air. The height, h, in feet above the ground is given by h = -16t² + 123t + 40. How long is the rock in the air? Example: Ellen kicks a stone off the edge of a tall cliff. The distance, d, between the rock and the ground t seconds after being kicked is d = -16t² - 6t + 480. How many seconds elapse before the rock is at height of 424 ft above the ground? Example: A ball is kicked in the air. The height of the ball, d, after t seconds is given by d = -16t² + 36t + 9. How long is the ball in the air to the nearest hundredth of a second?